The problem of transient Magnetohydrodynamic (MHD) combined convection within a wavy-heated rectangular cavity having two inner cylinders is investigated using the non-homogeneous nanofluid scheme. The lower wavy surface of the cavity is kept at a constant hot temperature ($T_h$) while the upper flat surface is kept at a constant cold temperature ($T_c$). The remaining surfaces (vertical surfaces) are maintained adiabatic. An ${\mathrm{Al}}_2{\mathrm{O}}_3$/water nanofluid is filled inside the cavity and a non-homogeneous approach is adopted to solve governing equations by using the Galerkin method. The effect of some parameters such as the angular rotational speed, the volume fraction of nanoparticles, Hartmann number on the flow and heat transfer characteristics are examined. The results indicate that the waving of the hot base of the cavity enhances the Nusselt number. The maximal Nusselt numbers are obtained when the number of undulations N is 2, where the Nusselt number augments by 18% when N is boosted from 0 to 2 and by 16% from 0 to and 5. Also, the outcomes reveal that the enhancement of the Nusselt number as a result of raising the rotational speed of the two cylinders from 0 to ± 500 is about 315%.

使用非均匀纳米流体方案研究了具有两个内圆柱体的波浪形加热矩形腔内的瞬态磁流体动力学 (MHD) 组合对流问题。型腔的下波浪面保持恒定的高温（${吨}_H$) 而上平面保持在恒定的低温下 (${吨}_C$）。其余表面（垂直表面）保持绝热。一个${\mathrm{铝}}_2{\mathrm{哦}}_3$腔内填充/水纳米流体，采用非齐次方法求解控制方程，采用伽辽金法。考察了角转速、纳米颗粒的体积分数、哈特曼数等参数对流动和传热特性的影响。结果表明，型腔热基部的波动提高了努塞尔数。当起伏数N为 2时获得最大 Nusselt 数，其中当N从 0 增加到 2时，Nusselt 数增加了 18%，从 0 到 5 增加了 16%。此外，结果表明将两个气缸的转速从 0 提高到 ± 500 的结果的努塞尔数约为 315%。